The same applicant is owner of Spanish patent application number 9600632, which discloses a mechanism for sliding glass doors in which an upper rail and a lower guide parallel to the former participate, between which a fixed leaf and a shiftable leaf are situated, the upper rail, starting from a general inverted L-shape, having means for attaching stops limiting the run of the shiftable leaf, a rib which is longitudinal and oriented upward for the shifting of wheels associated to the shiftable leaf, and said shiftable leaf especially having a pair of suspension heads, in addition to incorporating respective wheels, each one of which heads configures a type of grip susceptible to being fixed to the upper edge of the shiftable leaf without needing holes or any other type of machining of the latter, specifically by simple tightening of said grip and by means of introducing sheets of an anti-slipping material between the grip and the shiftable leaf.